Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV-2) can cause the life-threatening acute respiratory disease called COVID-19 (Coronavirus Disease 2019) as well as debilitating multiorgan dysfunction that persists after the initial viral phase has resolved. Long COVID or Post-Acute Sequelae of COVID-19 (PASC) is manifested by a variety of symptoms, including fatigue, dyspnea, arthralgia, myalgia, heart palpitations, and memory issues sometimes affecting between 30% and 75% of recovering COVID-19 patients. However, little is known about the mechanisms causing Long COVID and there are no widely accepted treatments or therapeutics. After introducing the clinical aspects of acute COVID-19 and Long COVID in humans, we summarize the work in animals (mice, Syrian hamsters, ferrets, and nonhuman primates (NHPs)) to model human COVID-19. The virology, pathology, immune responses, and multiorgan involvement are explored. Additionally, any studies investigating time points longer than 14 days post infection (pi) are highlighted for insight into possible long-term disease characteristics. Finally, we discuss how the models can be leveraged for treatment evaluation, including pharmacological agents that are currently in human clinical trials for treating Long COVID. The establishment of a recognized Long COVID preclinical model representing the human condition would allow the identification of mechanisms causing disease as well as serve as a vehicle for evaluating potential therapeutics.